The killer was aged 37, and had arrived in France in 2019 as an immigrant without papers, before being given leave to remain, said the source, who added that he ‘was not known to anti-terrorist officers.’
The source said: "The attack happened just after 2pm. The administrative officer was pounced on by the man, who slit her throat with a knife.
"The assailant was shot dead by police officers soon afterwards, as efforts were made to save the victim."
The local prosecutor's office later announced that the officer had died.
Yvan Assioma, of the Alliance Police Union, said the officer was a 49-year-old mum-of-two, who died at the scene.
The officer was surprised by the attacker as she returned from lunch, a source told Le Parisien.
The attacker had lived in France since 2009, the report added.
French Interior Minister Gerald Darmanin, who was travelling to the scene, wrote on Twitter: "A police officer was the victim of a knife attack at the Rambouillet police station."
Prime Minister Jean Castex was also on his way to the scene, with President Emmanuel Macron out of the country.
A tweet on the Twitter account for the SCPN, a union which represents national police officers, stated: "The National Police is once again bereaved by a despicable attack.
"Support for the family and loved ones of our colleague.
"All police officers of all ranks and all bodies know that to serve is to risk one's life in the face of fanaticism and extremists."
Local prosecutors were leading the investigation.
Home to about 26,000 people, Rambouillet is about 40 miles south-west of Paris.
Friday's incident follows six years of savage Islamist attacks in France, including the beheading of schoolteacher Samuel Paty by a Russian-born terrorist in October last year.
The deadliest single terrorist attack ever in the country came in November 2015 when 130 people were killed in Paris.
Suicide bombers pledging allegiance to ISIS targeted the Stade de France, cafes, restaurants and the Bataclan music venue, where 90 died.
Earlier in the year, two Paris-born gunmen linked to al-Qaeda broke into the offices of the Charlie Hebdo satirical magazine, leaving 12 dead and 11 wounded.
In July 2016, 86 people were killed and more than 400 injured when a 19-tonne truck was deliberately driven into crowds on the seafront promenade at Nice, in the South of France.
The terrorist turned out to be a radicalised Tunisian immigrant who was shot dead by police.
During the same month, two ISIS terrorists murdered an 86-year-old Catholic priest during a church service in Normandy.
There have been frequent knife attacks on the forces of law and order, leading to the deaths of serving police.
In October 2019, a radicalised computer operative working at the Paris Prefecture in central Paris stabbed four of his colleagues to death.
The attacker – who was also shot dead – turned out to be a Muslim convert who kept extremist al-Qaeda and Islamic State literature and images on his computer.
